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Question

# A circular plate of diameter a, is kept in contact with a square plate of side a as shown in figure. The density of the material and thickness are same everywhere. The centre of mass of the composite system will be :

A
Inside the circular plate
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B
Inside the square plate
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C
At the point of contact
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D
Outside the system
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Solution

## The correct option is B Inside the square plateConsidering origin (0,0) at the point of contact of the given plates. Due to symmetry about x−axis, the centre of mass of system will lie on the x−axis. Area of circular plate, A1=π(a2)2 x - coordinate of COM, x1=−a2 Area of square plate, A2=a2 x - coordinate of COM, x2=+a2 ⇒xCM=A1x1+A2x2A1+A2 ⇒xCM=π(a2)2×(−a2)+a2(a2)π(a2)2+a2 ∴xCM=a(4−π)2(π+4) It clearly shows that xCM>0, hence COM of composite system lies inside the square plate.

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